Glow Discharges in Inert and Reactive Gases

So far we used the terms plasma and discharge or glow discharge already several times without giving a clear definition. In the following and also in daily live of materials processing the two terms were used synonymously because both were linked to the subject of more or less ionized gases. In the world of physics the terms are handled rather different (indeed a real physicist would not like such a sloppy nomenclature). The concept of plasmas is very general and applied to describe phenomena involving charges from outer space to conducting electrons in metals. A plasma is very homogenous without edge effects, it can be characterized by two parameters, its density $n$ and temperature $T$. On the other hand, the glow discharges which are the subject of our discussion are rather different. E. g. they have clear boundaries, called sheaths^1.2 and instead of one temperature, different temperatures for electrons, ions and neutrals may be defined. But before going into details, one thing should be mentioned: Even if typical discharges in materials processing are far away from being an ideal plasma, many concepts developed here can be applied on a qualitative or semi quantitative basis also to glow discharges. The following definition of a plasma is given by Chen [2]:

A plasma is a quasi-neutral gas of charged and neutral particles which exhibits collective behavior.

Before the sentence above is meaningful we have to further define quasi-neutral and collective behaviour, a task which is rather difficult based on the material which we already covered. Therefore we will start by some heurisitic arguments and everything will be covered again later in a greater depth.

Let us consider an arbitrary neutral gas where no macroscopic forces act on the constituents (gravity is negligible), then their motion is controlled just by collisions among them. A macroscopic force like e. g. the compression of the gas is transmitted by those collisions to the individual atoms or molecules. In case of the before mentioned example of compression the number of collisions would increase. This situation changes totally if we allow our particles to carry electrical charges. This moving charges create electric fields, currents and magnetic fields which influence other particles far away. This is meant by collective behaviour.

The just given explanation was already rather empiric, but our situation for quasi neutrality is even worse. One important characteristic of plasmas is their capability to shield out electrical potentials applied to them by redistributing their charged constituents. It is possible to calculate a characteristic length, called Debye length $\lambda_d$, over which the imposed electric potential decays. With this knowledge we can now define quasi neutrality which requires the following conditions to be satisfied:

• The Debye length $\lambda_d$ must be much smaller than the system dimension $L$:

  
  

  $$\lambda_d \ll L.$$
  
  

• The Debye shielding is a statistical concept where many charged particles are required to cancel the electrical potential. So the number of particles $N_d$ in a sphere with a radius of $\lambda_d$ must be sufficiently high:

  
  

  $$N_d \gg 1.$$
  
  

• Finally on macroscopic scales the plasma must be basically neutral, means the number of positive (ions) and negative (electrons) charges must be nearly equal:

  
  

  $$n_i \simeq n_e \simeq n.$$
  
  

After finishing this a bit dry tasting, but very important definitions, we should have a look on the roadmap for the rest of this section. First we will review the ideal gas, especially the relationship between the macroscopic properties and the individual movement of its constituents (kinetic gas theory). Next collisions among the particles in the plasma will be considered as they are substantial for sustaining the plasma via ionization. Then there is a more practical part concerning vacuum technology, before we switch back to the electrical characteristics of plasmas addressing mobility and plasma potential.